1. Field of the Invention
The present invention relates to acoustic analysis of liquids, and more particularly to the use of resonant ultrasonic fields to determine the concentration of a dissolved species.
2. Description of the Related Art
Just as electromagnetic energy has been widely exploited in the measurement of physicochemical properties of gases, liquids and solids, so too have sound waves. Ultrasound, in the upper kilohertz and megahertz frequency bands, has proven especially useful for studying liquids. The acoustic properties of a liquid -- in particular, the velocity and attenuation of an ultrasonic pressure wave through the liquid -- depend on, and therefore can be used to measure, various thermodynamic and kinetic characteristics. Sound velocity, for example, provide information about adiabatic compressibility and density. Attenuation of sound in the medium provides information about the kinetic and thermodynamic parameters of relaxation processes. Both the velocity and attenuation of ultrasound are frequently observed to monitor chemical processes occurring in solution and to determine solute concentrations.
A wide variety of ultrasonic instrumentation has been developed for specialized research purposes. Essentially, these instruments include means for generating a sound wave in the material to be studied, and means for measuring reporting changes in the sound wave as it propagates through and interacts with the material. Devices intended to analyze liquids generally make use of a pair of piezoelectric transducers, one of which generates the acoustic signal and the other of which detects the signal after it has traveled through the liquid under study. The acoustic signal may take many forms, e.g., a pulse wave, a continuous traveling wave or a continuous standing wave; the frequency of the applied field may be varied or kept constant; and the measured parameters may include amplitude, phase and/or frequency.
Plane-wave resonators are a common type of instrument for ultrasonic analysis of liquids. These devices may comprise a chamber having plane piezotransducers along two opposed, precisely parallel walls. A plane pressure wave is generated by one transducer and progresses through the liquid to the other transducer, where it is detected and reflected back to the first transducer. At certain fundamental frequencies determined primarily by the distance between transducers and the acoustic properties of the contained liquid, the traveling transmitted and reflected waves combine into the stationary pattern characteristic of a standing wave. The standing wave condition results in delivery by the detection transducer of large voltage peaks.
In operation, once the standing wave is achieved, one changes the applied frequency and plots (or otherwise monitors) the amplitude and phase at the detecting transducer as a function of applied frequency. This information facilitates calculation of the primary acoustic parameters of the liquid, namely, the velocity and attenuation of sound. These parameters, in turn, can provide information on characteristics such as concentration. The plane-wave resonator has also been used to measure the thermodynamic properties of a liquid (since the velocity of sound is a simple function of the second derivative of free energy with respect to pressure, and therefore the profile of sound velocity at different temperatures and pressures can be used to derive the equation of state).
Acoustic absorption occurs as a result of irreversible interaction of ultrasonic pressure waves with a liquid and/or with a chemical species in the liquid. To distinguish between the absorption due to the pure liquid and to a dissolved species, one compares the absorption characteristics of the solution against that of the pure solvent, both measured at the same temperature and in the same resonator cell. The degree to which absorption of the solution exceeds that of the pure solvent reflects the contribution of the solute, and therefore its concentration.
To measure absorption using the plane-wave resonator, one typically activates the driven transducer and adjusts the frequency until a standing wave is observed. The amplitude and resonance frequency fn are measured at peak output voltage (resonance) and at oscillation frequencies above and below resonance where the amplitude falls 3 db below peak (the half-power level). This procedure is executed for the pure solvent and, separately, for the sample under study.
An important characteristic of a resonator is its quality factor, Q, defined as the ratio of the resonance frequency to the half-power frequency band, f.sub.n /.DELTA.f.sub.n. Q is inversely proportional to the total energy loss in the resonator system, which includes, in addition to attenuation due to the liquid, losses from beam divergence, scattering, friction, imperfect reflection, and transducer mounting and coupling. High Q-factors are associated with symmetry and smoothness of sharp resonance peaks and definite separations of resonance peaks in the frequency scale.
Solute concentration may be derived from comparison of the measured Q-factors of the pure solvent and that of the solution. Investigations of fast chemical reactions and relaxation processes occurring in solution, by contrast, generally involve measurement of the absorption over a range of frequencies.
Measurements of acoustic velocity in a liquid are made primarily to evaluate elastic properties, such as compressibility. The natural resonance frequencies of a liquid-containing resonator are linearly related to the ultrasound velocity. These frequencies may be determined by identifying output-voltage maxima (as described above) or by determining the inflection points of a phase-frequency plot. For solutions, the relative difference between sound velocities in a reference liquid (e.g., a pure solvent) and a sample liquid (e.g., a solution) is a linear function of the relative difference between resonance frequencies of the liquids according to the relation EQU (V.sub.s -V.sub.r)/V.sub.r =(f.sub.ns -f.sub.nr)/f.sub.nr
where V.sub.r is the velocity of sound in the reference liquid, V.sub.s is the velocity in the sample liquid, and f.sub.nr and f.sub.ns are resonance frequencies of the reference and sample liquids, respectively. The sound velocity of a sample is calculated using resonance-frequency measurements and knowledge of the sound velocity in the reference liquid.
Plane-wave resonators, while common, suffer from a number of disadvantages, one of which is the necessity for complex constructions to achieve and maintain the parallelism conditions required to support standing waves. Plots of amplitude as a function of frequency obtained with improperly adjusted plane-wave resonators often exhibit field distortions, which may be manifested as "humps" indicative of the presence of unwanted interference effects, spurious modes, reflective side walls, or misalignment of the plane transducers. This is due in large part to the mechanical difficulty of achieving and maintaining precise alignment among the various resonator components. Also, the production of adequate standing-wave patterns requires transducer diameters that are much larger than the wavelength (typically, the ratio of diameter to wavelength exceeds 20), thus placing relatively large lower limits on resonator volumes.
Resonators of all types are vulnerable to temperature drift, since the fluid wavelength of sound in the fluid is highly temperature-dependent. Thermostating capability, therefore, is frequently crucial. For example, in water, a change of 1.degree. C. alters the speed of sound by approximately 0.15%, altering the resonance wavelength by the same proportion; this shift is significantly greater than the resonance range, and will therefore drive the system out of resonance. For example, using a water-filled resonator operating at a resonance frequency of 10 MHz, the half-power bandwidth (i.e., the effective resonance range) is approximately 1 kHz; a change in temperature of as little as 0.066.degree. C. is sufficient to drive the system outside this bandwidth. See Eggers et al., "Ultrasonic Measurements with Milliliter Liquid Samples in the 0.5-100 MHz Range," 44 Rev. Sci. Instr. 969 (1973).